Find the exact value of the given expression.
sin(2cos^{-1} 24/25)
_______
Find the exact value of the given expression.
sec(2 sin^{-1} 1/8)
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ANSWER :
9.
sin(2 cos^(-1) 24 / 25)
Let cos^(-1) 24 / 25 = x
=> cos(x) = 24/25 .
So,
sin(2 cos^(-1) 24 / 25)
= sin(2x)
= 2 sin(x) cos(x)
= 2 sqrt(1 - coś^2 x) coś(x)
= 2 sqrt( 1 - (24/25)^2) * 24 / 25
= 2 * sqrt((625-576) / 625) * 24 / 25
= 2 * sqrt(49 / 625) * 24 / 25
= 2* 7 / 25 * 24 / 25
= 336 / 625 (ANSWER).
10.
sec(2 sin^(-1) 1 / 8 )
Let sin((-1) 1 / 8 = x
=> 1/8 = sin(x)
=> cos(x) = sqrt( 1 - (1/8)^2) = sqrt(63 / 64)
=> cos^2 (x) = 63/64
Now,
sec(2 sin^(-1) 1 / 8)
= sec (2x)
= 1/cos(2x)
= 1 / (2cos^2 (x) - 1)
= 1 / (2*63/64 - 1)
= 1 / (62 / 64)
= 64/62
= 32/31 (ANSWER).
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